Multi-objective optimization method for structure parameters of superconducting cable, and device and medium

Abstract

The present invention relates to a multi-objective optimization method for structure parameters of a superconducting cable, and a device and a medium. The method comprises the following steps: S1, acquiring structure parameters and performance parameters of a superconducting cable, setting constraint ranges of the structure parameters of the superconducting cable, constructing objective functions on the basis of the structure parameters and the performance parameters of the superconducting cable, and establishing a multi-objective optimization model of the structure parameters of the superconducting cable; and S2, iteratively solving the multi-objective optimization model of the structure parameters of the superconducting cable by means of an improved multi-objective grey wolf optimization algorithm to obtain optimal solutions of the structure parameters of the superconducting cable, wherein weight coefficients negatively correlated with the overall sensitivity indexes of the structure parameters of the superconducting cable are assigned to iteration coefficients in the multi-target grey wolf optimization algorithm so as to obtain the improved multi-target grey wolf optimization algorithm. Compared with the prior art, the present invention can further improve the optimization speed and optimization effect of structure parameters of superconducting cables.

Description

A multi-objective optimization method, device and medium for superconducting cable structural parameters Technical Field

[0001] The present invention belongs to the technical field of power transmission and distribution, and in particular relates to a multi-objective optimization method, equipment and medium for superconducting cable structural parameters. Background Art

[0002] During operation, superconducting cables generate hysteresis losses due to the magnetic field transformation caused by alternating current. To maintain the normal operating temperature of the superconducting cable, the cooling system needs to consume at least 15 times the electrical energy to remove the heat generated by this AC loss from the system. Therefore, optimizing the cable structure to reduce AC losses and thus control the system cooling cost is an important factor to consider in the design of superconducting cable structures. In addition to affecting cooling costs, optimizing the cable structure also directly affects the amount of superconducting tape used. The production and preparation costs of superconducting tape are relatively high, so properly controlling the amount of tape used is also very critical. Research has shown that increasing the tape winding angle can reduce AC losses, but this also increases the amount of tape used. To obtain the optimal superconducting cable structure, it is necessary to balance multiple objective functions.

[0003] Chinese patent application CN202210369373.0 discloses a rapid optimization method for the structure of a superconducting cable. Using a particle swarm optimization algorithm (PSO), the algorithm rapidly optimizes the structural parameters of a cold-insulated high-temperature superconducting cable. This method accurately obtains the structural parameters of the cable, improving the efficiency and accuracy of the cable's R&D. While PSO performs well in terms of convergence speed, it can be slowed down when dealing with large-scale optimization problems due to the need to calculate the velocities and positions of a large number of particles. Furthermore, if particles in the PSO converge prematurely to a local optimum during the search process, particularly when dealing with complex multimodal function optimization problems, the entire swarm may become trapped in a local optimum and fail to find a global optimal solution. The multi-objective gray wolf optimization algorithm (MOGWO algorithm), which simulates the hunting behavior of gray wolves, focuses on maintaining a diverse solution space during the optimization process. It is easy to understand and apply, and is often used to solve complex multi-parameter, multi-objective optimization problems such as superconducting cable structure optimization. However, when using the MOGWO algorithm to optimize superconducting cable structures, the greater the number of tape layers, the more parameters involved, the more tedious the algorithm's iterative screening process becomes, and the computational time increases exponentially. Therefore, improvements to the MOGWO algorithm are needed to increase its convergence speed and optimization effectiveness when solving superconducting cable structural parameter optimization problems.

[0004] Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a multi-objective optimization method, equipment and medium for superconducting cable structural parameters, so as to improve the optimization speed and optimization effect of superconducting cable structural parameters.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A multi-objective optimization method for superconducting cable structural parameters comprises the following steps:

[0008] S1. Obtaining structural parameters and performance parameters of a superconducting cable, setting constraint ranges for each structural parameter of the superconducting cable, constructing an objective function based on the structural parameters and performance parameters of the superconducting cable, and establishing a multi-objective optimization model for the structural parameters of the superconducting cable;

[0009] S2. Iteratively solving the multi-objective optimization model of the superconducting cable structural parameters by using an improved multi-objective grey wolf optimization algorithm to obtain an optimal solution for the superconducting cable structural parameters;

[0010] The improved multi-objective grey wolf optimization algorithm is obtained by assigning a weight coefficient that is negatively correlated with the overall sensitivity index of each structural parameter of the superconducting cable to the iteration coefficient in the multi-objective grey wolf optimization algorithm.

[0011] Furthermore, the structural parameters of the superconducting cable include the number of tapes in each layer of the superconducting cable, the winding angle of each layer, and the radius of the innermost conductive layer.

[0012] Furthermore, the objective function includes the superconducting cable AC loss and the superconducting tape length.

[0013] Furthermore, the iteration coefficients in the multi-objective grey wolf optimization algorithm include one or more of the individual position contraction and expansion coefficient A and the individual's active exploration degree C within a certain random range around itself.

[0014] Furthermore, the multi-objective optimization model of the superconducting cable structural parameters is analyzed by the Sobol analysis method to obtain the overall sensitivity index of each structural parameter of the superconducting cable.

[0015] Furthermore, the multi-objective optimization model for superconducting cable structural parameters includes multiple objective functions, and Sobol analysis is performed on each objective function to obtain the overall sensitivity index of each structural parameter of the superconducting cable under each objective function, and the weight coefficient is generated based on the inverse of the average value of the overall sensitivity index of all objective functions.

[0016] Furthermore, the specific process of iteratively solving the multi-objective optimization model of the superconducting cable structural parameters by using the improved multi-objective grey wolf optimization algorithm is as follows:

[0017] S201, randomly generate an initial population, perform non-dominated sorting on the initial population, and establish a non-dominated solution set Archive;

[0018] S202, updating the iteration coefficient in the multi-objective grey wolf optimization algorithm based on the weight coefficient generated by the overall sensitivity index of each structural parameter of the superconducting cable;

[0019] S203, updating the position of each individual in the population based on the iteration coefficient, and updating the non-dominated solution set Archive;

[0020] S204, determine whether the iteration termination condition is met, if so, proceed to step S205; if not, return to step S203;

[0021] S205 , outputting the non-dominated solution set Archive, calculating the Euclidean distance after the fitness normalization of each non-dominated solution, and selecting the non-dominated solution with the smallest Euclidean distance as the optimal solution to be output.

[0022] Furthermore, in step S204, the iteration termination condition is reaching a preset maximum number of iterations.

[0023] The present invention also provides an electronic device, comprising a memory, a processor, and a program stored in the memory, wherein the processor implements the above method when executing the program.

[0024] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the program implements the above method when executed by a processor.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. The present invention assigns a weight coefficient based on the inverse of the overall sensitivity index of each structural parameter of the superconducting cable to the iteration coefficient in the multi-objective Grey Wolf optimization algorithm, thereby obtaining an improved multi-objective Grey Wolf optimization algorithm to solve the multi-parameter, multi-objective complex optimization problem of superconducting cable structural parameter optimization. The superconducting cable structural parameters that have a greater impact on the objective function use a smaller iteration coefficient during the iteration process, thereby improving the search accuracy within the constraint range and avoiding missing the optimal solution; at the same time, the superconducting cable structural parameters that have a smaller impact on the objective function use a larger iteration coefficient during the iteration process, thereby covering the entire constraint space more quickly, accelerating the optimization speed, and avoiding falling into a local optimal solution; the improved multi-objective Grey Wolf optimization algorithm performs personalized iterations for different superconducting cable structural parameters, and can significantly improve the convergence speed and optimization effect of the multi-objective Grey Wolf optimization algorithm in solving the multi-objective superconducting cable structural parameter optimization problem.

[0027] 2. The present invention analyzes the multi-objective optimization model of superconducting cable structural parameters through the Sobol analysis method to obtain the overall sensitivity index of each structural parameter of the superconducting cable. It can effectively determine the key structural parameters that affect the performance of the multi-objective optimization model of superconducting cable structural parameters and analyze the interaction effects between each structural parameter, which facilitates the understanding and optimization of complex nonlinear multi-objective models. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] FIG1 is a flow chart of the method of the present invention;

[0029] FIG2 is a flow chart of the improved multi-objective gray wolf optimization algorithm;

[0030] Figure 3 is the AC loss Sobol analysis result diagram;

[0031] Figure 4 is a diagram showing the Sobol analysis results for strip length;

[0032] Figure 5 shows the convergence results of the multi-objective grey wolf optimization algorithm before and after optimization of different iteration coefficients.

[0033] Among them, (5a) represents the unoptimized situation, (5b) represents the situation where only the individual position contraction and expansion coefficient A is optimized, (5c) represents the situation where only the individual's active exploration degree C within a certain random range around itself is optimized, and (5d) represents the situation where both the individual position contraction and expansion coefficient A and the individual's active exploration degree C within a certain random range around itself are optimized. DETAILED DESCRIPTION

[0034] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0035] Example 1

[0036] This embodiment provides a multi-objective optimization method for superconducting cable structural parameters, which optimizes the structural parameters of a 35kV / 2.2kA three-phase turnkey superconducting cable, as shown in FIG1 , including the following steps:

[0037] S1. Obtain the structural parameters and performance parameters of the superconducting cable, set the constraint range of each structural parameter of the superconducting cable, construct the objective function based on the structural parameters and performance parameters of the superconducting cable, and establish a multi-objective optimization model for the structural parameters of the superconducting cable.

[0038] The 35kV / 2.2kA three-phase turnkey superconducting cable contains four layers of superconducting tape, which are, from the outside to the inside, the superconducting tape-shielding layer, the insulating layer, the superconducting tape-conducting layer, and the semi-conducting layer. In this embodiment, the number of tapes in each layer is set to n1, n2, n3, and n4, respectively. The winding angles of each layer are θ1, θ2, θ3, and θ4, respectively. The radius of the innermost layer is R, with a total of 9 structural parameters. The superconducting cable AC loss Q and the superconducting tape length Length are used as the two objective functions to establish a multi-objective optimization model for the superconducting cable structural parameters. The specific calculation formulas for the two objective functions are as follows: Q = Q N +Q mag i ac =I / I c

[0039] Among them, Q N is the self-field transmission loss of the superconducting tape, N i is the number of strips per layer, f is the frequency, μ0 is the vacuum permeability, I is the strip load current, I c is the critical current of the superconducting tape, i ac is the normalized current, Q mag is the external field magnetization loss of the superconducting cable, B i is the magnetic induction intensity, β i Normalized magnetic field, S i is the cross-sectional area of ​​the superconducting tape, J C is the critical current density of the superconducting tape, b is half the width of the superconducting tape, L0 is the cable length, θ i is the winding angle of the i-th layer.

[0040] The calculation results are then compared in the form of Euclidean distance to select the optimal solution:

[0041] Due to the limitation of tape stress, the range of winding angles θ1, θ2, θ3, and θ4 of each layer is set to 5°-35°; due to the limitation of the cross-sectional area of ​​the copper skeleton of the superconducting cable, the range of winding radius R of the innermost tape is set to 11.45mm-12.45mm; due to the limitation of superconducting tape width and critical current density under a certain winding radius, the range of the number of tape roots n1, n2, n3, and n4 in each layer is ([11,14], [11,14], [19,22], [20,23]) respectively.

[0042] S2. The multi-objective optimization model of superconducting cable structural parameters is iteratively solved by the improved multi-objective grey wolf optimization algorithm to obtain the optimal solution of the superconducting cable structural parameters.

[0043] In the multi-objective gray wolf optimization algorithm (MOGWO), the core iterative process (the process of encircling prey in gray wolf pack hunting behavior) is the process of adjusting the positions X of other individuals based on the positions of the three optimal leader solutions α, β, and δ. The iterative process of adjusting the individual position X based on the position of the α solution is used as an example (the iterative process based on the β and δ solutions is the same, only the subscripts are changed), as shown in the following formula:

[0044] Where D represents the distance between the individual and the location of the α solution, t is the iterative number, t max is the maximum number of iterations, which is set to 300 in this embodiment. α (t) is the position of the α solution in the tth generation, X(t) is the position of other individuals being solved in the tth generation, a is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases, r1 and r2 are random numbers between [0,1], so A is the coefficient representing the contraction and expansion of the individual position, and its range of variation is [-2,2]. That is, when |A|>1, the individual will move away from the α wolf position, and when |A|<1, the individual will move closer to the α wolf position, that is, the first half of the optimization tends to search the entire space, and the second half tends to converge to the optimal solution. C represents the degree of active exploration of the individual within a certain random range around itself.

[0045] The next positions of the three leaders α, β, and δ are combined to update the next generation positions X(t+1) of other individuals, as shown in the following formula:

[0046] As can be seen from the above formula, for each structural parameter in the superconducting cable, the iteration coefficients A and C in the iterative process are all the same value, and the global search is also performed with the same step size. However, in studying the influence of a single variable on the AC loss of superconducting cables, it was found that different parameters have different degrees of influence on the AC loss. Therefore, the iteration process should also be adjusted differently based on the sensitivity of different parameters. The present invention uses the normalized overall sensitivity of each parameter obtained by Sobol analysis to assign weight coefficients to the iteration coefficients in the random iteration process, as shown in the following formula:

[0047] Among them, S T1 、S T2 ,……,S Tn Represents the normalized overall sensitivity index of each parameter.

[0048] The Sobol analysis method is used to analyze the multi-objective optimization model of superconducting cable structural parameters, and the sensitivity analysis results under the two objective functions are shown in Figures 2 and 3 respectively. It can be seen that in the two-objective function calculation model, the first-order sensitivity index distribution of the 9 input structural parameters is relatively disordered due to the high nonlinearity in the calculation process. The overall sensitivity index of the structural parameters in the two-objective function calculation model generally shows a trend of gradual increase. This shows that when considering the interaction and nonlinear relationship between the parameters, the calculation model has made a more comprehensive and specific response to different parameters: the number of superconducting tapes in each layer can generally affect the AC loss more significantly than the winding angle of each layer. Therefore, the average value of the overall sensitivity index of the two objective functions is taken as the optimization basis for the coefficients, as follows:

[0049] Through the above adjustments, the parameters that have a greater impact on the objective function can use smaller random values ​​during the iteration process, so as to improve the search accuracy of the parameters within the constraint range and avoid missing the optimal solution; at the same time, the parameters that have a smaller impact on the objective function can use larger random values ​​during iteration, covering the entire constraint space more quickly, thereby speeding up the optimization process and avoiding falling into the local optimal solution.

[0050] The optimized MOGWO algorithm flow is shown in FIG4 . The specific process of iteratively solving the multi-objective optimization model of the superconducting cable structural parameters by the improved multi-objective Grey Wolf optimization algorithm is as follows:

[0051] S201, randomly generate an initial population, perform non-dominated sorting on the initial population, discard dominated solutions, retain non-dominated solutions, and establish a non-dominated solution set Archive;

[0052] S202, updating the iteration coefficient in the multi-objective grey wolf optimization algorithm based on the weight coefficient generated by the overall sensitivity index of each structural parameter of the superconducting cable;

[0053] S203, updating the position of each individual in the population based on the iteration coefficient, and updating the non-dominated solution set Archive;

[0054] S204: Determine whether the maximum number of iterations has been reached. If so, proceed to step S205; if not, return to step S203.

[0055] S205 , outputting the non-dominated solution set Archive, calculating the Euclidean distance after the fitness normalization of each non-dominated solution, and selecting the non-dominated solution with the smallest Euclidean distance as the optimal solution to be output.

[0056] The improved algorithm performs personalized iterations for different superconducting cable structural parameters, which can significantly improve the convergence speed and optimization effect of the MOGWO algorithm in solving the multi-objective superconducting cable structural parameter optimization problem. In order to verify the effectiveness of the method of the present invention, the convergence and iteration effects of the traditional MOGWO algorithm (coefficients A and C are not optimized), only optimizing coefficient A, only optimizing coefficient C, and optimizing coefficients A and C at the same time are compared. The results are shown in (5a), (5b), (5c) and (5d) of Figure 5 respectively. Due to the limitation of random numbers in the intelligent optimization algorithm, the speed of iterative convergence to the optimal solution and the optimal solution converged to may be different in each optimization process. Therefore, the structural parameter optimization in each case was carried out three times. It can be seen that the number of iterations required for the traditional MOGWO algorithm to converge to the optimal solution ranges from approximately 120 to 200. After optimizing coefficient A three times, the optimization procedure converges to the optimal solution within a stable number of iterations below 50, significantly improving the convergence speed and achieving good convergence results. However, optimizing coefficient C three times does not improve the convergence speed and may even prevent convergence to the optimal solution, resulting in poor optimization results. After optimizing both coefficients A and C three times, the number of iterations required for the optimization procedure to converge to the optimal solution ranges from approximately 100 to 200, with insignificant convergence speed improvements and unstable optimization results. The above comparison shows that optimizing coefficient A in the MOGWO algorithm optimization procedure can significantly improve the convergence speed and optimization results of the MOGWO algorithm.

[0057] In order to verify the accuracy of the convergence results of the proposed MOGWO algorithm based on the improved coefficient A, the optimization results obtained by the MOGWO algorithm with the improved coefficient A are compared with the 35kV / 2.2kA three-phase turnkey superconducting cable structure in operation in the existing literature (Zhang Xize, Zong Xihua, Huang Yijia. Design research of kilometer-level superconducting cables in Shanghai [J]. Cryogenics and Superconductivity, 2022, 50(06): 35-41). The results are shown in Table 1.

[0058] Table 1 Structural parameters of three-phase turnkey superconducting cable before and after optimization

[0059] As shown in Table 1, the structural parameters obtained by the improved MOGWO algorithm based on the optimization coefficient A generally show little error compared to the structural parameters of three-phase all-in-one superconducting cables obtained in existing literature (i.e., the reference values ​​in the table). In summary, this invention, based on the traditional MOGWO algorithm for handling nonlinear multi-objective models, assigns a weighting coefficient based on parameter sensitivity to the iteration coefficient A. This helps the global optimization algorithm explore the space and converge actively, thereby finding the global optimal solution more quickly and effectively. This can significantly improve the optimization speed and effectiveness in practical multi-parameter and multi-objective optimization problems.

[0060] Example 2

[0061] This embodiment provides an electronic device including one or more processors and a memory, wherein the memory stores one or more programs that can execute instructions for all or part of the steps of the multi-objective optimization method for superconducting cable structural parameters as described in Example 1.

[0062] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for superconducting cable structural parameters, characterized in that: The following steps are involved: S1. Obtaining structural parameters and performance parameters of a superconducting cable, setting constraint ranges for each structural parameter of the superconducting cable, constructing an objective function based on the structural parameters and performance parameters of the superconducting cable, and establishing a multi-objective optimization model for the structural parameters of the superconducting cable; S2. Iteratively solving the multi-objective optimization model of the superconducting cable structural parameters by using an improved multi-objective grey wolf optimization algorithm to obtain an optimal solution for the superconducting cable structural parameters; The improved multi-objective grey wolf optimization algorithm is obtained by assigning a weight coefficient that is negatively correlated with the overall sensitivity index of each structural parameter of the superconducting cable to the iteration coefficient in the multi-objective grey wolf optimization algorithm.

2. The multi-objective optimization method for superconducting cable structural parameters according to claim 1, characterized in that: The structural parameters of the superconducting cable include the number of tapes in each layer of the superconducting cable, the winding angle of each layer, and the radius of the innermost conductive layer.

3. The multi-objective optimization method for superconducting cable structural parameters according to claim 1, characterized in that: The objective function includes the superconducting cable AC loss and the superconducting tape length.

4. The multi-objective optimization method for superconducting cable structural parameters according to claim 1, characterized in that: The iteration coefficients in the multi-objective gray wolf optimization algorithm include one or more of the individual position contraction and expansion coefficient A and the individual's active exploration degree C within a certain random range around itself.

5. The multi-objective optimization method for superconducting cable structural parameters according to claim 1, characterized in that: The multi-objective optimization model of the superconducting cable structural parameters is analyzed by the Sobol analysis method to obtain the overall sensitivity index of each structural parameter of the superconducting cable.

6. The multi-objective optimization method for superconducting cable structural parameters according to claim 5, characterized in that: The multi-objective optimization model for superconducting cable structural parameters includes multiple objective functions. Sobol analysis is performed on each objective function to obtain an overall sensitivity index of each structural parameter of the superconducting cable under each objective function. The weight coefficient is generated based on the inverse of the average value of the overall sensitivity index of all objective functions.

7. The multi-objective optimization method for superconducting cable structural parameters according to claim 1, characterized in that: The specific process of iteratively solving the multi-objective optimization model of the superconducting cable structural parameters by the improved multi-objective Grey Wolf optimization algorithm is as follows: S201, randomly generate an initial population, perform non-dominated sorting on the initial population, and establish a non-dominated solution set Archive; S202, updating the iteration coefficient in the multi-objective grey wolf optimization algorithm based on the weight coefficient generated by the overall sensitivity index of each structural parameter of the superconducting cable; S203, updating the position of each individual in the population based on the iteration coefficient, and updating the non-dominated solution set Archive; S204, determine whether the iteration termination condition is met, if so, proceed to step S205; if not, return to step S203; S205 , outputting the non-dominated solution set Archive, calculating the Euclidean distance after the fitness normalization of each non-dominated solution, and selecting the non-dominated solution with the smallest Euclidean distance as the optimal solution to be output.

8. The multi-objective optimization method for superconducting cable structural parameters according to claim 7, characterized in that: In step S203, the iteration termination condition is reaching a preset maximum number of iterations.

9. An electronic device comprising a memory, a processor, and a program stored in the memory, wherein: When the processor executes the program, the method according to any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 8 is implemented.

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